**24 - Amazon Top Interview Questions**

### Problem Statement :

You are given a list of four integers nums, each between 0 and 9, in a fixed order. By placing the operators +, -, *, and / (where / is integer division) between the numbers, and grouping them with parentheses, determine whether it is possible to get the value 24. Constraints n = 4 where n is the length of nums 0 ≤ nums[i] ≤ 9 Example 1 Input nums = [5, 2, 7, 8] Output True Explanation We can do (5 * 2 - 7) * 8 = 24 Example 2 Input nums = [7, 9, 7, 4] Output True Explanation We can make 24 with (7 - (9 / 7)) * 4. Note that / is integer division so the result of 9 / 7 is floored.

### Solution :

` ````
Solution in C++ :
vector<int> count(vector<int>& nums, int l, int r) {
if (l == r) return {nums[l]};
vector<int> ret;
for (int j = l; j < r; j++) {
vector<int> left = count(nums, l, j);
vector<int> right = count(nums, j + 1, r);
for (auto& n : left) {
for (auto& p : right) {
ret.push_back(n + p);
ret.push_back(n * p);
ret.push_back(n - p);
if (p != 0) ret.push_back(n / p);
}
}
}
return ret;
}
bool solve(vector<int>& nums) {
int l = 0, r = 3;
auto dos = count(nums, l, r);
int ret = 0;
for (auto& n : dos) ret += n == 24;
return ret > 0;
}
```

` ````
Solution in Java :
import java.util.*;
class Solution {
char[] ops = {'+', '-', '*', '/'};
public boolean solve(int[] nums) {
return check(nums);
}
private boolean check(int[] arr) {
if (arr.length == 1) {
return arr[0] == 24;
}
for (int i = 0; i < arr.length - 1; i++) {
for (char op : ops) {
int[] res = operate(arr, i, op);
if (check(res)) {
return true;
}
}
}
return false;
}
private int[] operate(int[] orig, int idx, char op) {
int[] res = new int[orig.length - 1];
for (int i = 0; i < idx; i++) {
res[i] = orig[i];
}
if (op == '+') {
res[idx] = orig[idx] + orig[idx + 1];
} else if (op == '-') {
res[idx] = orig[idx] - orig[idx + 1];
} else if (op == '*') {
res[idx] = orig[idx] * orig[idx + 1];
} else {
res[idx] = orig[idx + 1] == 0 ? 0 : orig[idx] / orig[idx + 1];
}
for (int i = idx + 2; i < orig.length; i++) {
res[i - 1] = orig[i];
}
return res;
}
}
```

` ````
Solution in Python :
class Solution:
def solve(self, nums):
self.res = False
def go(i, ops, postfix):
# no. of ops. used is never more than
# index
if i == 4 and ops == 3:
if self.postorder_eval(postfix) == 24:
self.res = True
if ops < i - 1:
for op in "+-/*":
postfix.append(op)
go(i, ops + 1, postfix)
postfix.pop()
if i < len(nums):
postfix.append(nums[i])
go(i + 1, ops, postfix)
postfix.pop()
return
go(0, 0, [])
return self.res
# postfix is easy to evaluate and no brackets ;)
def postorder_eval(self, postfix):
res = []
for c in postfix:
if isinstance(c, str):
b = int(res.pop())
a = int(res.pop())
if c == "+":
c = a + b
elif c == "-":
c = a - b
elif c == "*":
c = a * b
elif c == "/":
if b == 0:
c = 0
else:
c = a // b
res.append(c)
else:
res.append(c)
return res[-1]
```

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